Quadratic Function Word Problems

Rescue Dog Day

Today (May 20th) is National Rescue Dog Day!

Liza works at a dog shelter and wants to see how much money the dog shelter makes on this national holiday. The profit $y$ is found based on how much rescued dogs cost today at the shelter. The shelter's goal is to make $1,000$ dollars today while selling the dogs at the cheapest price possible. The equation that models profit for the shelter is $y=21x^{2}-260x-500$
where $x$ is the price per dog. What is the cheapest the dogs could be sold for while achieving a goal of $1,000$ dollar profit? (Round your answer to the nearest whole number.)